Question: Solve for $x$ and $y$ using elimination. ${4x-6y = -2}$ ${-5x-3y = -29}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${4x-6y = -2}$ $10x+6y = 58$ Add the top and bottom equations together. $14x = 56$ $\dfrac{14x}{{14}} = \dfrac{56}{{14}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {4x-6y = -2}\thinspace$ to find $y$ ${4}{(4)}{ - 6y = -2}$ $16-6y = -2$ $16{-16} - 6y = -2{-16}$ $-6y = -18$ $\dfrac{-6y}{{-6}} = \dfrac{-18}{{-6}}$ ${y = 3}$ You can also plug ${x = 4}$ into $\thinspace {-5x-3y = -29}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - 3y = -29}$ ${y = 3}$